Abstract
In the uncapacitated asymmetric traveling salesman problem with multiple stacks, one first performs a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then delivers every item by performing a second hamiltonian circuit. Here, we are interested in the convex hull of the arc-incidence vectors of such couples of hamiltonian circuits.
For the general case, we determine the dimension of this polytope, and show that every facet of the asymmetric traveling salesman polytope defines one of its facets. For the special case with two stacks, we provide an integer linear programming formulation whose linear relaxation is polynomial-time solvable, and we propose new families of valid inequalities to reinforce the latter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alba, M., Cordeau, J.-F., Dell’Amico, M., Iori, M.: A Branch-and-Cut Algorithm for the Double Traveling Salesman Problem with Multiple Stacks. INFORMS Journal on Computing (2011) (published online)
Bonomo, F., Mattia, S., Oriolo, G.: Bounded coloring of co-comparability graphs and the pickup and delivery tour combination problem. Theoretical Computer Science 412(45), 6261–6268 (2011)
Carrabs, F., Cerulli, R., Speranza, M.G.: A Branch-and-Bound Algorithm for the Double TSP with Two Stacks. Technical report (2010)
Casazza, M., Ceselli, A., Nunkesser, M.: Efficient algorithms for the double traveling salesman problem with multiple stacks. Computers & Operations Research 39, 1044–1053 (2012)
Felipe, A., Ortuno, M.T., Tirado, G.: The Double Traveling Salesman Problem with Multiple Stacks: A Variable Neighborhood Search Approach. Computers & Operations Research 36, 2983–2993 (2009)
Gutan, G., Punnen, A.P.: The Traveling Salesman Problem and Its Variations. In: Combinatorial Optimization, vol. 12. Kluwer Academic Publishers (2002)
Lusby, R.M., Larsen, J., Ehrgott, M., Ryan, D.: An exact method for the double TSP with multiple stacks. International Transactions on Operations Research 17, 637–652 (2010)
Petersen, H.L., Archetti, C., Sperenza, M.G.: Exact Solutions to the Double Travelling Salesman Problem with Multiple Stacks. Networks 56(4), 229–243 (2010)
Petersen, H.L., Madsen, O.B.G.: The double travelling salesman problem with multiple stacks - Formulation and heuristic solution approaches. European Journal of Operation Research 198(1), 139–147 (2009)
Pnueli, A., Lempel, A., Even, S.: Transitive orientation of graphs and identification of permutation graphs. Canadian Journal of Mathematics 23, 160–175 (1971)
Toulouse, S.: Approximability of the Multiple Stack TSP. In: International Symposium on Combinatorial Optimization (ISCO 2010), ENDM 813-820 (2010)
Toulouse, S., Wolfler Calvo, R.: On the Complexity of the Multiple Stack TSP, kSTSP. In: Chen, J., Cooper, S.B. (eds.) TAMC 2009. LNCS, vol. 5532, pp. 360–369. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borne, S., Grappe, R., Lacroix, M. (2012). The Uncapacitated Asymmetric Traveling Salesman Problem with Multiple Stacks. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-32147-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32146-7
Online ISBN: 978-3-642-32147-4
eBook Packages: Computer ScienceComputer Science (R0)